The square root of 961 is expressed as √961 in the radical form and as (961)½ or (961)0.5 in the exponent form. The square root of 961 is 31. It is the positive solution of the equation x2 = 961. The number 961 is a perfect square.

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**Square Root of 961:**31

**Square Root of 961 in exponential form:**(961)½ or (961)0.5

**Square Root of 961 in radical form:**√961

1. | What is the Square Root of 961? |

2. | How to find the Square Root of 961? |

3. | Is the Square Root of 961 Rational? |

4. | FAQs |

The square root of 961, (or root 961), is the number which when multiplied by itself gives the product as 961. Therefore, the square root of 961 = √961 = 31.

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### Value of √961 by Long Division Method

**Explanation:**

Therefore, the square root of 961 by long division method is 31.

## Is Square Root of 961 Rational?

The value of √961 is 31. Hence, the square root of 961 is a rational number.

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## Square Root of 961 Solved Examples

**Example 1: Solve the equation x2 − 961 = 0**

**Solution:**

x2 - 961 = 0 i.e. x2 = 961x = ±√961Since the value of the square root of 961 is 31,⇒ x = +√961 or -√961 = 31 or -31.

**Example 3: If the area of a circle is 961π in2. Find the radius of the circle.**

**Solution:**

Let "r" be the radius of the circle.⇒ Area of the circle = πr2 = 961π in2⇒ r = ±√961 inSince radius can"t be negative,⇒ r = √961Square root of 961 is 31.⇒ r = 31 in

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## FAQs on the Square Root of 961

### What is the Value of the Square Root of 961?

The square root of 961 is 31.

### Why is the Square Root of 961 a Rational Number?

Upon prime factorizing 961 i.e. 312, we find that all the prime factors are in even power. This implies that the square root of 961 is a positive integer. Therefore, the square root of 961 is rational.

### What is the Square Root of -961?

The square root of -961 is an imaginary number. It can be written as √-961 = √-1 × √961 = i √961 = 31iwhere i = √-1 and it is called the imaginary unit.

### If the Square Root of 961 is 31. Find the Value of the Square Root of 9.61.

See more: Closed Circle On A Number Line, Basic Linear Inequalities

Let us represent √9.61 in p/q form i.e. √(961/100) = 9.61/10 = 3. Hence, the value of √9.61 = 3

### What is the Square Root of 961 in Simplest Radical Form?

We need to express 961 as the product of its prime factors i.e. 961 = 31 × 31 . Therefore, as visible, the radical form of the square root of 961 cannot be simplified further. Therefore, in the simplest radical form of the square root of 961 can be written as √961.

### Evaluate 5 plus 10 square root 961

The given expression is 5 + 10 √961. We know that the square root of 961 is 31. Therefore, 5 + 10 √961 = 5 + 10 × 31 = 5 + 310 = 315